Problem: $\dfrac{ 9h + 10i }{ -9 } = \dfrac{ h + 7j }{ -4 }$ Solve for $h$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ 9h + 10i }{ -{9} } = \dfrac{ h + 7j }{ -4 }$ $-{9} \cdot \dfrac{ 9h + 10i }{ -{9} } = -{9} \cdot \dfrac{ h + 7j }{ -4 }$ $9h + 10i = -{9} \cdot \dfrac { h + 7j }{ -4 }$ Multiply both sides by the right denominator. $9h + 10i = -9 \cdot \dfrac{ h + 7j }{ -{4} }$ $-{4} \cdot \left( 9h + 10i \right) = -{4} \cdot -9 \cdot \dfrac{ h + 7j }{ -{4} }$ $-{4} \cdot \left( 9h + 10i \right) = -9 \cdot \left( h + 7j \right)$ Distribute both sides $-{4} \cdot \left( 9h + 10i \right) = -{9} \cdot \left( h + 7j \right)$ $-{36}h - {40}i = -{9}h - {63}j$ Combine $h$ terms on the left. $-{36h} - 40i = -{9h} - 63j$ $-{27h} - 40i = -63j$ Move the $i$ term to the right. $-27h - {40i} = -63j$ $-27h = -63j + {40i}$ Isolate $h$ by dividing both sides by its coefficient. $-{27}h = -63j + 40i$ $h = \dfrac{ -63j + 40i }{ -{27} }$ Swap signs so the denominator isn't negative. $h = \dfrac{ {63}j - {40}i }{ {27} }$